我在一次工作面试中被问到这个问题,我想知道其他人是如何解决这个问题的。我最擅长使用Java,但也欢迎使用其他语言的解决方案。

给定一个数字数组nums,返回一个数字数组products,其中products[i]是所有nums[j]的乘积,j != i。 输入:[1,2,3,4,5] 输出:[(2 * 3 * 4 * 5),(1 * 3 * 4 * 5),(1 * 2 * 4 * 5),(1 * 2 * 3 * 5),(1 * 2 * 3 * 4)] = [120, 60, 40, 30, 24] 你必须在O(N)中不使用除法来做这个。


当前回答

下面是Ruby中的一行程序解决方案。

全国矿工工会。映射{|n| (num - [n]).inject(:*)}

其他回答

将Michael Anderson的解决方案翻译成Haskell:

otherProducts xs = zipWith (*) below above

     where below = scanl (*) 1 $ init xs

           above = tail $ scanr (*) 1 xs
public static void main(String[] args) {
    int[] arr = { 1, 2, 3, 4, 5 };
    int[] result = { 1, 1, 1, 1, 1 };
    for (int i = 0; i < arr.length; i++) {
        for (int j = 0; j < i; j++) {
            result[i] *= arr[j];

        }
        for (int k = arr.length - 1; k > i; k--) {
            result[i] *= arr[k];
        }
    }
    for (int i : result) {
        System.out.println(i);
    }
}

我想出了这个解决方案,我发现它很清楚,你觉得呢!?

这是ptyhon版本

  # This solution use O(n) time and O(n) space
  def productExceptSelf(self, nums):
    """
    :type nums: List[int]
    :rtype: List[int]
    """
    N = len(nums)
    if N == 0: return

    # Initialzie list of 1, size N
    l_prods, r_prods = [1]*N, [1]*N

    for i in range(1, N):
      l_prods[i] = l_prods[i-1] * nums[i-1]

    for i in reversed(range(N-1)):
      r_prods[i] = r_prods[i+1] * nums[i+1]

    result = [x*y for x,y in zip(l_prods,r_prods)]
    return result

  # This solution use O(n) time and O(1) space
  def productExceptSelfSpaceOptimized(self, nums):
    """
    :type nums: List[int]
    :rtype: List[int]
    """
    N = len(nums)
    if N == 0: return

    # Initialzie list of 1, size N
    result = [1]*N

    for i in range(1, N):
      result[i] = result[i-1] * nums[i-1]

    r_prod = 1
    for i in reversed(range(N)):
      result[i] *= r_prod
      r_prod *= nums[i]

    return result

使用EcmaScript 2015编码

'use strict'

/*
Write a function that, given an array of n integers, returns an array of all possible products using exactly (n - 1) of those integers.
*/
/*
Correct behavior:
- the output array will have the same length as the input array, ie. one result array for each skipped element
- to compare result arrays properly, the arrays need to be sorted
- if array lemgth is zero, result is empty array
- if array length is 1, result is a single-element array of 1

input array: [1, 2, 3]
1*2 = 2
1*3 = 3
2*3 = 6
result: [2, 3, 6]
*/
class Test {
  setInput(i) {
    this.input = i
    return this
  }
  setExpected(e) {
    this.expected = e.sort()
    return this
  }
}

class FunctionTester {
  constructor() {
    this.tests = [
      new Test().setInput([1, 2, 3]).setExpected([6, 3, 2]),
      new Test().setInput([2, 3, 4, 5, 6]).setExpected([3 * 4 * 5 * 6, 2 * 4 * 5 * 6, 2 * 3 * 5 * 6, 2 * 3 * 4 * 6, 2 * 3 * 4 * 5]),
    ]
  }

  test(f) {
    console.log('function:', f.name)
    this.tests.forEach((test, index) => {
      var heading = 'Test #' + index + ':'
      var actual = f(test.input)
      var failure = this._check(actual, test)

      if (!failure) console.log(heading, 'input:', test.input, 'output:', actual)
      else console.error(heading, failure)

      return !failure
    })
  }

  testChain(f) {
    this.test(f)
    return this
  }

  _check(actual, test) {
      if (!Array.isArray(actual)) return 'BAD: actual not array'
      if (actual.length !== test.expected.length) return 'BAD: actual length is ' + actual.length + ' expected: ' + test.expected.length
      if (!actual.every(this._isNumber)) return 'BAD: some actual values are not of type number'
      if (!actual.sort().every(isSame)) return 'BAD: arrays not the same: [' + actual.join(', ') + '] and [' + test.expected.join(', ') + ']'

      function isSame(value, index) {
        return value === test.expected[index]
      }
  }

  _isNumber(v) {
    return typeof v === 'number'
  }
}

/*
Efficient: use two iterations of an aggregate product
We need two iterations, because one aggregate goes from last-to-first
The first iteration populates the array with products of indices higher than the skipped index
The second iteration calculates products of indices lower than the skipped index and multiplies the two aggregates

input array:
1 2 3
   2*3
1*    3
1*2

input array:
2 3 4 5 6
    (3 * 4 * 5 * 6)
(2) *     4 * 5 * 6
(2 * 3) *     5 * 6
(2 * 3 * 4) *     (6)
(2 * 3 * 4 * 5)

big O: (n - 2) + (n - 2)+ (n - 2) = 3n - 6 => o(3n)
*/
function multiplier2(ns) {
  var result = []

  if (ns.length > 1) {
    var lastIndex = ns.length - 1
    var aggregate

    // for the first iteration, there is nothing to do for the last element
    var index = lastIndex
    for (var i = 0; i < lastIndex; i++) {
      if (!i) aggregate = ns[index]
      else aggregate *= ns[index]
      result[--index] = aggregate
    }

    // for second iteration, there is nothing to do for element 0
    // aggregate does not require multiplication for element 1
    // no multiplication is required for the last element
    for (var i = 1; i <= lastIndex; i++) {
      if (i === 1) aggregate = ns[0]
      else aggregate *= ns[i - 1]
      if (i !== lastIndex) result[i] *= aggregate
      else result[i] = aggregate
    }
  } else if (ns.length === 1) result[0] = 1

  return result
}

/*
Create the list of products by iterating over the input array

the for loop is iterated once for each input element: that is n
for every n, we make (n - 1) multiplications, that becomes n (n-1)
O(n^2)
*/
function multiplier(ns) {
  var result = []

  for (var i = 0; i < ns.length; i++) {
    result.push(ns.reduce((reduce, value, index) =>
      !i && index === 1 ? value // edge case: we should skip element 0 and it's the first invocation: ignore reduce
      : index !== i ? reduce * value // multiply if it is not the element that should be skipped
      : reduce))
  }

  return result
}

/*
Multiply by clone the array and remove one of the integers

O(n^2) and expensive array manipulation
*/
function multiplier0(ns) {
  var result = []

  for (var i = 0; i < ns.length; i++) {
    var ns1 = ns.slice() // clone ns array
    ns1.splice(i, 1) // remove element i
    result.push(ns1.reduce((reduce, value) => reduce * value))
  }

  return result
}

new FunctionTester().testChain(multiplier0).testChain(multiplier).testChain(multiplier2)

使用Node.js v4.4.5运行:

Node—harmony integerarrays.js

function: multiplier0
Test #0: input: [ 1, 2, 3 ] output: [ 2, 3, 6 ]
Test #1: input: [ 2, 3, 4, 5, 6 ] output: [ 120, 144, 180, 240, 360 ]
function: multiplier
Test #0: input: [ 1, 2, 3 ] output: [ 2, 3, 6 ]
Test #1: input: [ 2, 3, 4, 5, 6 ] output: [ 120, 144, 180, 240, 360 ]
function: multiplier2
Test #0: input: [ 1, 2, 3 ] output: [ 2, 3, 6 ]
Test #1: input: [ 2, 3, 4, 5, 6 ] output: [ 120, 144, 180, 240, 360 ]

试试这个!

import java.util.*;
class arrProduct
{
 public static void main(String args[])
     {
         //getting the size of the array
         Scanner s = new Scanner(System.in);
            int noe = s.nextInt();

        int out[]=new int[noe];
         int arr[] = new int[noe];

         // getting the input array
         for(int k=0;k<noe;k++)
         {
             arr[k]=s.nextInt();
         }

         int val1 = 1,val2=1;
         for(int i=0;i<noe;i++)
         {
             int res=1;

                 for(int j=1;j<noe;j++)
                 {
                if((i+j)>(noe-1))
                {

                    int diff = (i+j)-(noe);

                    if(arr[diff]!=0)
                    {
                    res = res * arr[diff];
                    }
                }

                else
                {
                    if(arr[i+j]!=0)
                    {
                    res= res*arr[i+j];
                    }
                }


             out[i]=res;

         }
         }

         //printing result
         System.out.print("Array of Product: [");
         for(int l=0;l<out.length;l++)
         {
             if(l!=out.length-1)
             {
            System.out.print(out[l]+",");
             }
             else
             {
                 System.out.print(out[l]);
             }
         }
         System.out.print("]");
     }

}